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Wednesday, December 30, 2009

To Do + Math on Vacation

The Mathniños at the Modern Wing

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Math Teachers at Play 22I'm hosting this months blog-carnival, and I'd love your submissions from your own blog or nominations from blogs you read. Submit nominations at the blogcarnival site, or using the widget at the bottom of the right column on this page.

An aside: I got to meet Math Mama over break and Sue was as nice and interesting as you'd think from her blog. We were going to meet up with Maria from Teaching College Math, but the weather prevented it (sorta).

Biggest Math Story of the YearTime Magazine has submitted that the proof of Langlands' Fundamental Lemma was the 7th Biggest Scientific Discovery of 2009. A quite technical exposition of the Lemma (not the proof) is here. (Hat tip Peter Woit of Not Even Wrong). I do not have an understanding of the math, but it concerns a connection between Galois group theory (about solutions to algebraic equations) and general linear algebra representation theory (think matrices on steroids). One of the most famous theorems that uses the Lemma has Femat's Last Theorem as a corollary. Powerful stuff.

It's nice for students to know that math is ongoing, and also to hear terms like lemma, theorem and corollary used genuinely. I also like how this emphasizes the power of connections in mathematics, and how even (or especially) the world's most powerful mathematician's start problem solving by solving simpler problems or finding another way to put the problem. It also should be noted that Ngo's proof was submitted in 2008, but took until this year to verify.

Math (Art) on VacationMy wife and I recently won tickets to the Cirque de Soleil show Banana Shpeel (which I would recommend.) On the quick trip to Chicago this week sans kids (hat tip: grandparents!) we had more time in the Art Institute than we would have had otherwise.

In the geometry class I've been writing about, we do one constructive project in which students build a polyhedron for the following context:

Hoity Toity, the upscale chain of Haute Couture for the masses, is having a competition to design new and original knick-knack boxes. Being an accomplished mathematician, you have an unfair advantage, which you intend to exploit to the maximum. Boxes must have a volume of at least 1 liter. (1000 cm3).

Students do a terrific job in general. One student this semester made a dog-shaped polyhedron. Cool. Some classic Archimedean solids, as well as prisms and antiprisms and such.

But at the Art Institute I had two ideas for new variations. The Modern Wing in itself is an inspiration as it is filled with beautiful proportions and rectangles with more connections and relationships than you could ever hope to count.

The Chess Set

This wonderfully sculpted set filled me with visions of two people working together to make a set of polyhedra vs non polyhedra. They could do found or constructed objects. It will require connections (what makes the difference between the king and queen, how will players know this is a rook, what's the difference in the bishops between the sides...) and analysis of the solids and their volume.

The Building

I so wanted to see the isometric drawings for this. I wouldn't insist that the building be built, which gives me pause, but I would want two different representations that would help someone build it. Students should design their own advanced building and think about it in scale

I'm curious to see where these ideas go, and what students make of them. I would like to hear more from other teachers about from where their ideas come, and the process they follow to implement them and refine them in the classroom. I think we teachers do a lot of our sharing as a product exchange.

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